Quantum Fisher Information: Probe to Measure Fractional Evolution

Abstract

We develop an analytical solution of fractional Schrodinger equation to explain the interaction between a two-level atom and a single electromagnetic field mode inside a cavity. Based on this solution, two different cases are discussed; the first one reflects the standard Jaynes Cummings model, while the second solution gives rise to a wave equation for a dipole interacted with a field in semi-classical sense. By controlling different parameters inside cavity, the estimation degree in terms of quantum Fisher information is investigated. The obtained results show that the precision estimation increases as the detuning decreases and number of photons inside cavity increases. Moreover robust estimation is obtained for the standard Jaynes Cummings model. To measure the amount of information, a comparative study between von Neumann entropy and quantum Fisher information show the same behavior. As a result, we conclude that quantum Fisher information may detect entanglement of the interacted atom-field system.